Most of the casualties from Saturday's earthquake are in the city of Muzaffarabad, the capital of Pakistani-controlled Kashmir.
Interior Minister Aftab Ahmed Sherpao says that Muzaffarabad was 70 percent destroyed.
"So far, the figures that we have, is 19,000 and 400 dead but it may increase by the hour and there are about 42,000 people injured. Some of these areas are still cut off and we do not have any communications. There have been villages which have been wiped out," he said.
Hundreds of deaths also are being reported in other parts of Pakistan and India.
Rescue workers say key roads remain blocked by debris and mudslides.
Soldiers are working around the clock trying to restore the main road linking Kashmir to the rest of Pakistan, to allow urgently needed aid to pass through.
Military planes are dropping supplies to some cut off areas and the government is setting up satellite telephones at 200 locations so that people in devastated areas could contact their families elsewhere in the country.
In Islamabad, Pakistan's President Pervez Musharaf asked the international community for assistance.
"We have tremendous manpower. What we do need is financial support so we can use it in any way we feel is required," said Mr. Musharaf. "Secondly, medicines and thirdly, tentage and blankets."
The president also says the country desperately needs helicopters to help ferry aid to victims in quake affected areas. They have only 29 available now.
Mr. Sherpao, the interior minister, says the United States promised to make available some of its military helicopters being used in neighboring Afghanistan.
Relief agencies are dispatching assessment teams to the hardest hit areas in Kashmir and the neighboring Northwest Frontier Province.
Authorities there say hundreds of children were killed when their schools collapsed. Hundreds more are still trapped beneath the rubble as rescue workers frantically try to dig them out.
Powerful aftershocks continue to rattle the country and officials say more tremors are expected in the days ahead.